A group of women who are taking legal action against police chiefs over claims they were tricked into forming long-term relationships with undercover spies have lost their fight to have part of their case heard in public.

Three appeal court judges ruled on Tuesday that the women's claims that their human rights were breached must be heard at the investigatory powers tribunal (IPT), often described as Britain's most secret court.

After the ruling, the women said the IPT was "an affront to the principles of natural justice and has only upheld a handful of claims in its history".

However, the women won another part of the case, concerning their other claims for damages under common law, including torts of misfeasance in public office, deceit, assault and negligence. In an earlier verdict, a judge had ruled that these common law claims should be stayed until after any hearing in the IPT. This stay was lifted on Tuesday by the three judges, meaning that the common law claims can be heard first.

The IPT was set up to hear complaints about unjustified surveillance by agencies such as MI5 and M16. Complainants have no automatic right to a hearing, to cross-examine witnesses, see the evidence or know why their case has been turned down.

Ten women brought the legal action after they discovered their partners were working for covert police units who had infiltrated political groups in an operation lasting more than four decades.

They say they suffered emotional trauma after they discovered the truth. Three women had relationships, one lasting six years, with Mark Kennedy, the undercover officer who infiltrated environmental campaigns for seven years.

On Tuesday, the master of the rolls Lord Dyson, Lord Justice Maurice Kay and Lady Justice Sharp said the IPT did have jurisdiction to decide all the human rights claims.

The police argued that the IPT, which was formed in 2000, was the appropriate forum for all the claims as parliament intended such cases to be decided by a specialist tribunal with a specially tailored procedure.

The women criticised the police for "obstructing our access to truth and justice by any means necessary, regardless of costs".